I second Beach Haven in LBI. My in-laws have a place there every summer and we love it with our 3 year old. Fantasy Island has an arcade and lots of kid friendly rides. Behind Fantasy Island is a water park with various water slides and wading pools. There are good restaurants and plenty of ice cream places and mini-golf. The beaches are nice and the area is pretty quiet. There's also an outside acoustic happy hour every weekend at the Engleside Motel that is great to go to with kids (not too loud).